How to get rid of vertice on the same high?
It seems you might have overlapping geometry, so you would have to solve that somehow if you wanted to have one piece of geometry. If the vertices are between edges on the same connected plane with nice non-overlapping topology, you can select all flat connected faces with Ctrl+Alt+Shift+f when you have one of them selected and then just press f for Make Face:



You could remove vertices from separate pieces of the mesh that you have there. If you wanted to join them into one piece, that is another question. I believe there is no easy clean way to do this, I would just remodel the whole thing as one if that is needed. Booleans might not work nicely if you have overlapping surfaces.